CN104881365A - RAID-6 extensible method based on erasure code similarity - Google Patents

Abstract

The invention provides an RAID-6 extensible method based on erasure code similarity. The invention discloses an entire set of architecture which is used for extending RAID-6 redundant arrays of inexpensive disks based on MDS codes and uniformly manages various MDS codes to achieve higher extensibility. In this architecture, a series of intermediate codes are further designed, and the intermediate codes are very easy to mutually convert, have characteristics of each MDS code and become a link for connecting the MDS codes together. The RAID-6 extensible method based on erasure code similarity can support flexible and high-efficiency scale extension of disk arrays. Compared with the traditional RAID extension scheme, the method has the advantages that the IO number is reduced by more than 44.1 percent, the time consumption is reduced by 95.2 percent and the data migration speed is improved by 20 times.

Description

Based on the RAID-6 expandable method of correcting and eleting codes similarity

Technical field

The present invention relates to a kind of RAID-6 expandable method based on correcting and eleting codes similarity.

Background technology

The probability of simultaneously makeing mistakes along with polydisc in storage system is more and more higher, redundant array of inexpensive disk, especially can support the RAID-6 array that double plate lost efficacy simultaneously, receive people's extensive concern.It is based on various correcting and eleting codes technology that traditional RAID-6 realizes, and a class be wherein referred to as ultimate range can the technology of Coded (MDS), more popular in RAID-6 system.MDS coding can be classified as level code and vertical code.Existing RAID-6 coding: the realization of RAID-6 coding is much based on correcting and eleting codes.Correcting and eleting codes can also be subdivided into two classes: maximum distance separable codes (MDS) and non-maximum distance separable codes (non-MDS).In RAID-6, ultimate range can be subdivided into two classes again by Coded: level code and vertical code.Level code includes Reed-Solomon Code, X-Code, HDP, H-Code, EVENODD, RDP etc.

The feature had desired by RAID-6 adjustment scale: when adjusting the scale of disk array, we need by more mobile data, and make after adjustment, the distribution of data on disk is still even.In the process of Data Migration, we more wish to keep uniform operating load on each disk, and mobile the least possible data block and check block.Here sum up at 6 in adjustment array scale, we wish the characteristic that adjustment algorithm can reach:

1) data are uniformly distributed, and each disk has data block and the check block of equal number, thus keep load balancing;

2) minimum data/check block moves.The minimum mobile quantity of theory increasing m block disk is and the minimum mobile number of the theory reducing m block disk is

3) immediate addressing, after completing disk adjustment scale, block physical address in an array still can calculate by very little cost;

4) minimum check disk amendment and calculating.In dilatation, one time data block moves the amendment that can bring its original check block, and the amendment of check block corresponding to reposition, and therefore this partial expense should be little as far as possible;

5) two-way expansion is supported.A desirable array scale adjustment algorithm, should support increase disk and reduce disk simultaneously;

6) smallest particles degree.Can support in any case to increase or reduce by one piece of disk.

Summary of the invention

The object of the present invention is to provide a kind of RAID-6 expandable method based on correcting and eleting codes similarity, disk array Expansion flexibly can be supported.

For solving the problem, the invention provides a kind of RAID-6 expandable method based on correcting and eleting codes similarity, comprising:

Encode for any one MDS, assuming that its name is called Code-X, support p+x block disk, p is prime number, 1≤x≤2, is that Code-X expands m block disk according to following rule, | m|≤3:

If-1≤x+m≤2, then from current MDS coding Code-X, point m expansion, expand one piece of disk, finally we can obtain S at every turn _p+x+m-Code, the path of expansion is Code-X → S _p+x-Code → S _p+x+1-Code →...→ S _p+x+m-Code, wherein, S _p+x-Code represents the coding of the check disk of p+x block disk, S _p+x+1-Code represents the coding of the check disk of p+x+1 block disk, S _p+x+m-Code represents the coding of the check disk of p+x+m block disk;

If x+m <-1 or x+m > 2, find satisfied-1≤x+m-(p-p')≤2 of p' that is new, expand to p'+x block disk from p+x block disk, then from current p'+x block disk, divide m expansion, expand one piece of disk at every turn.

Further, in the above-mentioned methods, for S _p-1the coded system of the check disk of-Code is as follows:

$\left\{\begin{array}{c}{C}_{i,i}=\underset{j=0}{\overset{p-2}{\mathrm{\&Sigma;}}}{C}_{i,j}(j\&NotEqual;i,j\&NotEqual;p-2-i)\\ C_{i,p-2-i}=\underset{j=0}{\overset{p-2}{\mathrm{\&Sigma;}}}{C}_{{\&lang;p-3-i-j\&rang;}_p,j}(j\&NotEqual;p-2-i)\end{array},\right.$

Wherein, 0≤i≤p-2,0≤j < n, n represent the quantity of expansion front disk array, and n is positive integer, C _i,irepresent the check block that in disk array, the i-th row i-th arranges, C _{i, p-2-i}the check block that in disk array, the i-th row p-2-i arranges, C _ijrepresent data block or the check block of the i-th row jth row in disk array, represent < p-3-i-j > in disk array _pthe data block of row jth row or check block.

Further, in the above-mentioned methods, S _p-1the equation of-Code decoding is as follows:

$\left\{\begin{array}{c}r={\&lang;p-3-i-f_1\&rang;}_p\\ C_{i,f_1}=C_{r,p-2-r}\&CirclePlus;\underset{j=0}{\overset{p-2}{\mathrm{\&Sigma;}}}{C}_{{\&lang;i+f_1-j\&rang;}_p,j}(j\&NotEqual;f_1,j\&NotEqual;{\&lang;i+f_1+1\&rang;}_p)\end{array}\right.,$

Wherein, the disk number of inefficacy is f ₁, the block that needs recover is

Further, in the above-mentioned methods, for S _pthe coded system of the check disk of-Code is as follows:

$\left\{\begin{array}{c}{C}_{i,p-1}=\underset{j=0}{\overset{p-2}{\mathrm{\&Sigma;}}}{C}_{i,j}\\ C_{i,p-2-i}=\underset{j=0}{\overset{p-2}{\mathrm{\&Sigma;}}}{C}_{{\&lang;p-3-i-j\&rang;}_p,j}(j\&NotEqual;p-2-i)\end{array},\right.$

Wherein, C _{i, p-1}represent the check block that in disk array, the i-th row p-1 arranges, C _{i, p-2-i}the check block that in disk array, the i-th row p-2-i arranges, C _ijrepresent data block or the check block of the i-th row jth row in disk array, represent < p-3-i-j > in disk array _pthe data block of row jth row or check block, < p-3-i-j > _prepresent the value of p-3-i-j p delivery.

Further, in the above-mentioned methods, S _pthe equation of-Code decoding is as follows:

$\left\{\begin{array}{c}r={\&lang;p-3-i-f_1\&rang;}_p\\ C_{i,f_1}=C_{r,p-2-r}\&CirclePlus;\underset{j=0}{\overset{p-2}{\mathrm{\&Sigma;}}}{C}_{{\&lang;i+f_1-j\&rang;}_p,j}(j\&NotEqual;f_1,j\&NotEqual;{\&lang;i+f_1+1\&rang;}_p)\end{array}\right..$

Further, in the above-mentioned methods, S _p+1the coded system of the check disk of-Code is as follows:

$\left\{\begin{array}{c}{C}_{i,p}=\underset{j=0}{\overset{p-2}{\mathrm{\&Sigma;}}}{C}_{i,j}\\ C_{i,p-i-1}=\underset{j=0}{\overset{p-1}{\mathrm{\&Sigma;}}}{C}_{{\&lang;p-3-i-j\&rang;}_p,j}(j\&NotEqual;p-1-i)\end{array},\right.$

Wherein, C _i,prepresent the check block that in disk array, the i-th row p arranges, C _{i, p-i-1}the check block that in disk array, the i-th row p-i-1 arranges, C _ijrepresent data block or the check block of the i-th row jth row in disk array, represent < p-3-i-j > in disk array _pthe data block of row jth row or check block.

Further, in the above-mentioned methods, S _p+1the decoding process of-Code is as follows:

$\left\{\begin{array}{c}r={\&lang;p-2-i-f_1\&rang;}_p\\ C_{i,f_1}=C_{r,p-1-r}\&CirclePlus;\underset{j=0}{\overset{p-1}{\mathrm{\&Sigma;}}}{C}_{{\&lang;i+f_1-j\&rang;}_p,j}(j\&NotEqual;f_1,j\&NotEqual;{\&lang;i+f_1+1\&rang;}_p)\end{array}\right..$

Compared with prior art, the present invention is by encoding for any one MDS, assuming that its name is called Code-X, support p+x block disk, p is prime number, 1≤x≤2, is that Code-X expands m block disk according to following rule, | m|≤3, if-1≤x+m≤2, then from current MDS coding Code-X, point m expansion, expand one piece of disk, finally we can obtain S at every turn _p+x+m-Code, the path of expansion is Code-X → S _p+x-Code → S _p+x+1-Code →...→ S _p+x+m-Code, wherein, S _p+x-Code represents the coding of the check disk of p+x block disk, S _p+x+1-Code represents the coding of the check disk of p+x+1 block disk, S _p+x+m-Code represents the coding of the check disk of p+x+m block disk; If x+m <-1 or x+m > 2, find satisfied-1≤x+m-(p-p')≤2 of p' that new, p'+x block disk is expanded to from p+x block disk, again from current p'+x block disk, divide m expansion, expand one piece of disk at every turn, flexible, efficient disk array Expansion can be supported

Accompanying drawing explanation

Fig. 1 is the three-layered node composition of the RAID-6 expandable method based on correcting and eleting codes similarity of one embodiment of the invention;

Fig. 2 is the decoding process schematic diagram of the S-code of one embodiment of the invention;

Fig. 3 be one embodiment of the invention from S _p-1-Code to S _pdilatation schematic diagram between-Code.

Embodiment

For enabling above-mentioned purpose of the present invention, feature and advantage become apparent more, and below in conjunction with the drawings and specific embodiments, the present invention is further detailed explanation.

The invention provides a kind of RAID-6 expandable method based on correcting and eleting codes similarity, comprising:

Encode for any one MDS, assuming that its name is called Code-X, support p+x block disk, p is prime number, 1≤x≤2, is that Code-X expands m block disk according to following rule, | m|≤3:

If-1≤x+m≤2, then from current MDS coding Code-X, point m expansion, expand one piece of disk, finally we can obtain S at every turn _p+x+m-Code, the path of expansion is Code-X → S _p+x-Code → S _p+x+1-Code →...→ S _p+x+m-Code, wherein, S _p+x-Code represents the coding of the check disk of p+x block disk, S _p+x+1-Code represents the coding of the check disk of p+x+1 block disk, S _p+x+m-Code represents the coding of the check disk of p+x+m block disk;

If x+m <-1 or x+m > 2, find satisfied-1≤x+m-(p-p')≤2 of p' that is new, expand to p'+x block disk from p+x block disk, then from current p'+x block disk, divide m expansion, expand one piece of disk at every turn.Concrete, encode (assuming that its name is called Code-X, supporting p+x block disk) for any one MDS, we are its expansion m block disk according to following rule:

(1) if-1≤x+m≤2, we are point m expansion just, expands one piece of disk at every turn.We are from current MDS coding, and finally we can obtain S _p+x+m-Code, and the path of expansion is: Code-X → S _p+x-Code → S _p+x+1-Code →...→ S _p+x+m-Code

(2) if x+m <-1 or x+m > 2, we need to find a new p' to meet-1≤x+m-(p-p')≤2.First, we expand to p'+x block disk from p+x block disk, and this process completes based on Code-X completely, and existing certain methods can help to accelerate this step.

In one preferred embodiment of the RAID-6 expandable method based on correcting and eleting codes similarity of the present invention, S _p-1the coded system of the check disk of-Code is as follows:

$\left\{\begin{array}{c}{C}_{i,i}=\underset{j=0}{\overset{p-2}{\mathrm{\&Sigma;}}}{C}_{i,j}(j\&NotEqual;i,j\&NotEqual;p-2-i)\\ C_{i,p-2-i}=\underset{j=0}{\overset{p-2}{\mathrm{\&Sigma;}}}{C}_{{\&lang;p-3-i-j\&rang;}_p,j}(j\&NotEqual;p-2-i)\end{array},\right.$

Wherein, 0≤i≤p-2,0≤j < n, n represent the quantity of expansion front disk array, and n is positive integer, C _i,irepresent the check block that in disk array, the i-th row i-th arranges, C _{i, p-2-i}the check block that in disk array, the i-th row p-2-i arranges, C _ijrepresent data block or the check block of the i-th row jth row in disk array, represent < p-3-i-j > in disk array _pthe data block of row jth row or check block.

In one preferred embodiment of the RAID-6 expandable method based on correcting and eleting codes similarity of the present invention, S _p-1the equation of-Code decoding is as follows:

$\left\{\begin{array}{c}r={\&lang;p-3-i-f_1\&rang;}_p\\ C_{i,f_1}=C_{r,p-2-r}\&CirclePlus;\underset{j=0}{\overset{p-2}{\mathrm{\&Sigma;}}}{C}_{{\&lang;i+f_1-j\&rang;}_p,j}(j\&NotEqual;f_1,j\&NotEqual;{\&lang;i+f_1+1\&rang;}_p)\end{array}\right.,$

Wherein, the disk number of inefficacy is f ₁, the block that needs recover is

In one preferred embodiment of the RAID-6 expandable method based on correcting and eleting codes similarity of the present invention, for S _pthe coded system of the check disk of-Code is as follows:

$\left\{\begin{array}{c}{C}_{i,p-1}=\underset{j=0}{\overset{p-2}{\mathrm{\&Sigma;}}}{C}_{i,j}\\ C_{i,p-2-i}=\underset{j=0}{\overset{p-2}{\mathrm{\&Sigma;}}}{C}_{{\&lang;p-3-i-j\&rang;}_p,j}(j\&NotEqual;p-2-i)\end{array},\right.$

Wherein, C _{i, p-1}represent the check block that in disk array, the i-th row p-1 arranges, C _{i, p-2-i}the check block that in disk array, the i-th row p-2-i arranges, C _ijrepresent data block or the check block of the i-th row jth row in disk array, represent < p-3-i-j > in disk array _pthe data block of row jth row or check block.

In one preferred embodiment of the RAID-6 expandable method based on correcting and eleting codes similarity of the present invention, S _pthe equation of-Code decoding is as follows:

$\left\{\begin{array}{c}r={\&lang;p-3-i-f_1\&rang;}_p\\ C_{i,f_1}=C_{r,p-2-r}\&CirclePlus;\underset{j=0}{\overset{p-2}{\mathrm{\&Sigma;}}}{C}_{{\&lang;i+f_1-j\&rang;}_p,j}(j\&NotEqual;f_1,j\&NotEqual;{\&lang;i+f_1+1\&rang;}_p)\end{array}\right..$

In one preferred embodiment of the RAID-6 expandable method based on correcting and eleting codes similarity of the present invention, S _p+1the coded system of the check disk of-Code is as follows:

$\left\{\begin{array}{c}{C}_{i,p}=\underset{j=0}{\overset{p-2}{\mathrm{\&Sigma;}}}{C}_{i,j}\\ C_{i,p-i-1}=\underset{j=0}{\overset{p-1}{\mathrm{\&Sigma;}}}{C}_{{\&lang;p-3-i-j\&rang;}_p,j}(j\&NotEqual;p-1-i)\end{array},\right.$

Wherein, C _i,prepresent the check block that in disk array, the i-th row p arranges, C _{i, p-i-1}the check block that in disk array, the i-th row p-i-1 arranges, C _ijrepresent data block or the check block of the i-th row jth row in disk array, represent < p-3-i-j > in disk array _pthe data block of row jth row or check block, < p-3-i-j > _prepresent the value of p-3-i-j p delivery.

In one preferred embodiment of the RAID-6 expandable method based on correcting and eleting codes similarity of the present invention, S _p+1the decoding process of-Code is as follows:

$\left\{\begin{array}{c}r={\&lang;p-2-i-f_1\&rang;}_p\\ C_{i,f_1}=C_{r,p-1-r}\&CirclePlus;\underset{j=0}{\overset{p-1}{\mathrm{\&Sigma;}}}{C}_{{\&lang;i+f_1-j\&rang;}_p,j}(j\&NotEqual;f_1,j\&NotEqual;{\&lang;i+f_1+1\&rang;}_p)\end{array}\right..$

Detailed, in order to overcome the adjustment scale problem of RAID-6 system, the present invention proposes a kind of unitized management MDS coding and supports the framework of two-way expansion (increasing/reduce disk).Fig. 1 illustrates the three-decker of the method, and the superiors are administration and supervision authorities, is then intermediate code layer, and bottom is MDS coding warehouse.

Administration and supervision authorities (Management Layer, ML) include the user interface that a unified management MDS encodes, and realize the code of array scale adjustment.The interface that administration and supervision authorities provide comprises the information providing MDS to encode, and provides the operation of increase disk/minimizing disk.

Intermediate code layer (Intermediate Code Layer, ICL) middle scalable coding (ScalableIntermediate Code is included, S-Code), this cover coding is RAID-6 system is p-1 in number of disks, solution during p, p+1, p+2 tetra-kinds of situations, i.e. four kinds of MDS codings, wherein p is a prime number.

We are denoted as S respectively these four kinds codings below _p-1-Code, S _p-Code, S _p+1-Code and S _p+2-Code.Have very similar design between these four kinds of S-Code, therefore the cost of conversion is very little mutually between which.Each S-Code can encode corresponding with the MDS in a kind of reality system, so we are by being easy to the S-Code mutually transformed, is linked together by multiple different MDS coding.

MDS Code Repos itory, MCR) include some existing MDS encoding schemes, such as EVENODD, RDP, H-Code, HDP etc.When a new MDS coding joins in coding warehouse, it and intermediate code contact and will be established.

The process of described disk expansion, we first define the expansion of two types, and one is efficient expansion (calling HE in the following text, High Efficiency), and the another kind of poor efficiency that cries expands (calling LE in the following text, Low Efficiency).HE can with the two-way expansion of little cost realization between MDS coding, and these costs comprise Data Migration amount, verification index word, calculated amount, etc.

Intermediate code layer: in this part, we introduce and are used for MDS to encode in the method the intermediate code S-Code connected.Very strong similarity is had between the S-Code being applicable to different disk quantity.The applicable number of disks of these four kinds of intermediate codes and mentality of designing following (setting p as a prime number):

S _p-1-Code: be applicable to p-1 block disk (a kind of mutation of HDP coding)

S _p-Code: be applicable to the p block disk (S of reduction version _p+1-Code)

S _p+1-Code: be applicable to p+1 block disk (mutation of a kind of H-Code)

S _p+2-Code: be applicable to p+1 block disk (i.e. EVENODD coding)

As shown in Figure 2, encoding and decoding: suppose C _ijrepresent data block or the check block of the i-th row jth row in disk array, wherein 0≤i≤p-2,0≤j < n.

S _p-1the coded system of the check disk of-Code is as follows:

$\left\{\begin{array}{c}{C}_{i,i}=\underset{j=0}{\overset{p-2}{\mathrm{\&Sigma;}}}{C}_{i,j}(j\&NotEqual;i,j\&NotEqual;p-2-i)\\ C_{i,p-2-i}=\underset{j=0}{\overset{p-2}{\mathrm{\&Sigma;}}}{C}_{{\&lang;p-3-i-j\&rang;}_p,j}(j\&NotEqual;p-2-i)\end{array}\right.$

S _p-1the equation of-Code decoding is following (supposes that the disk number lost efficacy is f ₁, the block that needs recover is ):

$\left\{\begin{array}{c}r={\&lang;p-3-i-f_1\&rang;}_p\\ C_{i,f_1}=C_{r,p-2-r}\&CirclePlus;\underset{j=0}{\overset{p-2}{\mathrm{\&Sigma;}}}{C}_{{\&lang;i+f_1-j\&rang;}_p,j}(j\&NotEqual;f_1,j\&NotEqual;{\&lang;i+f_1+1\&rang;}_p)\end{array}\right.$

For S _pthe coded system of the check disk of-Code is as follows:

$\left\{\begin{array}{c}{C}_{i,p-1}=\underset{j=0}{\overset{p-2}{\mathrm{\&Sigma;}}}{C}_{i,j}\\ C_{i,p-2-i}=\underset{j=0}{\overset{p-2}{\mathrm{\&Sigma;}}}{C}_{{\&lang;p-3-i-j\&rang;}_p,j}(j\&NotEqual;p-2-i)\end{array}\right.$

S _pthe decoding process of-Code is as follows:

$\left\{\begin{array}{c}r={\&lang;p-3-i-f_1\&rang;}_p\\ C_{i,f_1}=C_{r,p-2-r}\&CirclePlus;\underset{j=0}{\overset{p-2}{\mathrm{\&Sigma;}}}{C}_{{\&lang;i+f_1-j\&rang;}_p,j}(j\&NotEqual;f_1,j\&NotEqual;{\&lang;i+f_1+1\&rang;}_p)\end{array}\right.$

S _p+1the coded system of the check disk of-Code is as follows:

$\left\{\begin{array}{c}{C}_{i,p}=\underset{j=0}{\overset{p-2}{\mathrm{\&Sigma;}}}{C}_{i,j}\\ C_{i,p-i-1}=\underset{j=0}{\overset{p-1}{\mathrm{\&Sigma;}}}{C}_{{\&lang;p-3-i-j\&rang;}_p,j}(j\&NotEqual;p-1-i)\end{array}\right.$

S _p+1the decoding process of-Code is as follows:

$\left\{\begin{array}{c}r={\&lang;p-2-i-f_1\&rang;}_p\\ C_{i,f_1}=C_{r,p-1-r}\&CirclePlus;\underset{j=0}{\overset{p-1}{\mathrm{\&Sigma;}}}{C}_{{\&lang;i+f_1-j\&rang;}_p,j}(j\&NotEqual;f_1,j\&NotEqual;{\&lang;i+f_1+1\&rang;}_p)\end{array}\right..$

Observation for S-Code: carefully study the similarity between above-mentioned several S-Code, we can draw following observations:

1) change of data block quantity: for fixing prime number p, S _k-Code (p-1≤k≤p+2), namely has the S-Code of k disk, and in each encoding strip thereof, the quantity of data block is (p-1) × (k-2), and the constant number of check block is 2 (p-1);

2) change of chain length is verified: verification chain is defined as other data blocks involved by calculating of a check block or the set of check block.When the number of disks of S-Code changes, the length of verification chain also changes thereupon;

3) change of complicacy that check block generates increases with number of disks owing to verifying the length of chain, and complicacy of its coding also increases.

Unitized user management interface: unitized user management interface can provide the information of MDS coding in the method, and the flow process that increase, deletion MDS coding are provided.The MDS coded message that it provides contains encoding name, provides the quantity of disk, the equation of encoding and decoding, etc.The arthmetic statement of adding a coding is as follows:

Efficient expansion and poor efficiency are expanded: suppose in disk array, and total data volume is B, according to the spreading result of RAID-0, the basis of n block disk increase m block disk, and the amount that can reach the minimum Mobile data of Data distribution8 equilibrium is mB/ (n+m).Similarly, reduce m block disk from n block disk, in order to reach Data distribution8 equilibrium, minimum data mobile amount is | m|B/n.

In RAID-6, the capacity of equivalent and two pieces of disks is used as check block, and actual blocks of data occupies n-2 block disk, therefore optimum data or verification are moved when increasing and reduce m block disk, become respectively mB/ (n-2+m) and | m|B/ (n-2), can calculate thus, when increasing or reduce by one piece of disk, need the data total amount of movement to be about:

$\frac{1}{2}(\frac{B}{n-2+1}+\frac{B}{n-2})\&ap;\frac{B}{n-2}$

By this equation, we provide the definition of efficient expansion (HE):

Definition 1: for any two coding Code-X1 and Code-X2, suppose that these two kinds codings support p+x respectively ₁and p+x ₂block disk, and-1≤x ₁≤ x ₂≤ 2, | x ₁-x ₂|≤1, if data block and the check block amount of movement that (Code-X1 expands to Code-X2, or Code-X2 tapers to Code-X1) needs on any one conversion direction is no more than B/ (p-x ₁+ 2), the conversion so between them is just considered to efficient expansion, otherwise is then poor efficiency expansion.

Expansion algorithm: the expansion algorithm in the method comes from the difference in the general layout of different MDS coding.The difference of two kinds of codings is less, and expansion algorithm will be simpler.With reference to figure 3, following algorithm 2 describes the concrete steps (increase a blank diskette at first row, then the data of all the other disks moved past, thus ensure the equilibrium of Data distribution8) of this rapid translating.

In sum, the RAID-6 disk array based on MDS coding how is allowed to have good extended capability, it is a significant challenge facing of people instantly, in order to tackle this challenge, we have proposed a whole set of framework, for expanding the RAID-6 redundant array of inexpensive disk based on MDS coding, it manages multiple MDS uniformly and encodes, higher extendability is reached with this, in this framework, we have also been devised a series of intermediate code, these intermediate codes are very easy to conversion each other, there is the characteristic that each MDS encodes simultaneously, become the tie linked together of being encoded by these MDS, the present invention can support flexibly, efficient disk array Expansion, compared with traditional RAID expansion scheme, the method reduce the IO quantity of nearly 44.1%, reduce by the time loss of 95.2%, Data Migration speed is improved 20 times.

In this instructions, each embodiment adopts the mode of going forward one by one to describe, and what each embodiment stressed is the difference with other embodiments, between each embodiment identical similar portion mutually see.

Professional can also recognize further, in conjunction with unit and the algorithm steps of each example of embodiment disclosed herein description, can realize with electronic hardware, computer software or the combination of the two, in order to the interchangeability of hardware and software is clearly described, generally describe composition and the step of each example in the above description according to function.These functions perform with hardware or software mode actually, depend on application-specific and the design constraint of technical scheme.Professional and technical personnel can use distinct methods to realize described function to each specifically should being used for, but this realization should not thought and exceeds scope of the present invention.

Obviously, those skilled in the art can carry out various change and modification to invention and not depart from the spirit and scope of the present invention.Like this, if these amendments of the present invention and modification belong within the scope of the claims in the present invention and equivalent technologies thereof, then the present invention is also intended to comprise these change and modification.

Claims (7)

1., based on a RAID-6 expandable method for correcting and eleting codes similarity, it is characterized in that, comprising:

Encode for any one MDS, assuming that its name is called Code-X, support p+x block disk, p is prime number, 1≤x≤2, is that Code-X expands m block disk according to following rule, | m|≤3:

If-1≤x+m≤2, then from current MDS coding Code-X, point m expansion, expand one piece of disk, finally we can obtain S at every turn _p+x+m-Code, the path of expansion is Code-X → S _p+x-Code → S _p+x+1-Code →...→ S _p+x+m-Code, wherein, S _p+x-Code represents the coding of the check disk of p+x block disk, S _p+x+1-Code represents the coding of the check disk of p+x+1 block disk, S _p+x+m-Code represents the coding of the check disk of p+x+m block disk;

If x+m <-1 or x+m > 2, find satisfied-1≤x+m-(p-p')≤2 of p' that is new, expand to p'+x block disk from p+x block disk, then from current p'+x block disk, divide m expansion, expand one piece of disk at every turn.

2., as claimed in claim 1 based on the RAID-6 expandable method of correcting and eleting codes similarity, it is characterized in that, for S _p-1the coded system of the check disk of-Code is as follows:

$\left\{\begin{array}{c}{C}_{i,i}=\underset{j=0}{\overset{p-2}{\mathrm{\&Sigma;}}}{C}_{i,j}(j\&NotEqual;i,j\&NotEqual;p-2-i)\\ C_{i,p-2-i}=\underset{j=0}{\overset{p-2}{\mathrm{\&Sigma;}}}{C}_{{\&lang;p-3-i-j\&rang;}_{p,j}}(j\&NotEqual;p-2-i)\end{array}\right.,$

Wherein, 0≤i≤p-2,0≤j < n, n represent the quantity of expansion front disk array, and n is positive integer, C _i,irepresent the check block that in disk array, the i-th row i-th arranges, C _{i, p-2-i}the check block that in disk array, the i-th row p-2-i arranges, C _ijrepresent data block or the check block of the i-th row jth row in disk array, represent <p-3-i-j> in disk array _pthe data block of row jth row or check block, <p-3-i-j> _prepresent the value of p-3-i-j p delivery.

3., as claimed in claim 2 based on the RAID-6 expandable method of correcting and eleting codes similarity, it is characterized in that, S _p-1the equation of-Code decoding is as follows:

$\left\{\begin{array}{c}r={\&lang;p-3-i-f_i\&rang;}_p\\ C_{i,f_1}=C_{r,p-2-r}\&CirclePlus;\underset{j=0}{\overset{p-2}{\mathrm{\&Sigma;}}}{C}_{{\&lang;i+f_1-j\&rang;}_{p,j}}(j\&NotEqual;f_1,j\&NotEqual;\&lang;i+f_1+1{\&rang;}_p)\end{array}\right.,$

Wherein, the disk number of inefficacy is f ₁, need the block recovered to be C _{i, f1}.

4., as claimed in claim 3 based on the RAID-6 expandable method of correcting and eleting codes similarity, it is characterized in that, for S _pthe coded system of the check disk of-Code is as follows:

$\left\{\begin{array}{c}{C}_{i,p-1}=\underset{j=0}{\overset{p-2}{\mathrm{\&Sigma;}}}{C}_{i,j}\\ C_{i,p-2-i}=\underset{j=0}{\overset{p-2}{\mathrm{\&Sigma;}}}{C}_{{\&lang;p-3-i-j\&rang;}_{p,j}}(j\&NotEqual;p-2-i)\end{array}\right.,$

Wherein, C _{i, p-1}represent the check block that in disk array, the i-th row p-1 arranges, C _{i, p-2-i}the check block that in disk array, the i-th row p-2-i arranges, C _ijrepresent data block or the check block of the i-th row jth row in disk array, represent <p-3-i-j> in disk array _pthe data block of row jth row or check block.

5., as claimed in claim 4 based on the RAID-6 expandable method of correcting and eleting codes similarity, it is characterized in that, S _pthe equation of-Code decoding is as follows:

$\left\{\begin{array}{c}r={\&lang;p-3-i-f_i\&rang;}_p\\ C_{i,f_1}=C_{r,p-2-r}\&CirclePlus;\underset{j=0}{\overset{p-2}{\mathrm{\&Sigma;}}}{C}_{{\&lang;i+f_1-j\&rang;}_{p,j}}(j\&NotEqual;f_1,j\&NotEqual;\&lang;i+f_1+1{\&rang;}_p)\end{array}\right..$

6., as claimed in claim 5 based on the RAID-6 expandable method of correcting and eleting codes similarity, it is characterized in that, S _p+1the coded system of the check disk of-Code is as follows:

$\left\{\begin{array}{c}{C}_{i,p}=\underset{j=0}{\overset{p-2}{\mathrm{\&Sigma;}}}{C}_{i,j}\\ C_{i,p-i-1}=\underset{j=0}{\overset{p-1}{\mathrm{\&Sigma;}}}{C}_{{\&lang;p-3-i-j\&rang;}_{p,j}}(j\&NotEqual;p-1-i)\end{array}\right.,$

Wherein, C _i,prepresent the check block that in disk array, the i-th row p arranges, C _{i, p-i-1}the check block that in disk array, the i-th row p-i-1 arranges, C _ijrepresent data block or the check block of the i-th row jth row in disk array, represent <p-3-i-j> in disk array _pthe data block of row jth row or check block.

7., as claimed in claim 6 based on the RAID-6 expandable method of correcting and eleting codes similarity, it is characterized in that, S _p+1the decoding process of-Code is as follows:

$\left\{\begin{array}{c}r={\&lang;p-2-i-f_1\&rang;}_p\\ C_{i,f_1}=C_{r,p-1-r}\&CirclePlus;\underset{j=0}{\overset{p-1}{\mathrm{\&Sigma;}}}{C}_{{\&lang;i+f_1-j\&rang;}_{p,j}}(j\&NotEqual;f_1,j\&NotEqual;\&lang;i+f_1+1{\&rang;}_p)\end{array}\right..$